O que é a Função Densidade de Probabilidade ?

The Probability Density Function $f(x)$ of a continuous random variable defined in $\mathbb{R}$ is a function that represents the probability that the random variable takes a certain value in $\mathbb{R}$.

It makes logical sense that $\int_{-\infty}^{\infty} f(x) dx = 1$ since the probability that a function defined in $\mathbb{R}$ contains all its values between $-\infty$ and $\infty$ is $1$.